Results 1 to 10 of about 71 (31)

The agreement between novel exact and numerical solutions of nonlinear models

Partial Differential Equations in Applied Mathematics, 2023
Nonlinear models (NLMs), being an important topic in mathematical physics, have attracted a lot of attention in the international research community because they have numerous uses in human life. These NLMs are typically implemented to illuminate various
Md. Nur Alam, S. M. Rayhanul Islam
doaj   +1 more source

Estimates for evolutionary partial differential equations in classical function spaces

Forum of Mathematics, Sigma, 2023
We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations.
Alejandro J. Castro, Anders Israelsson, Wolfgang Staubach, Madi Yerlanov   +3 more
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On new computational and numerical solutions of the modified Zakharov–Kuznetsov equation arising in electrical engineering

Alexandria Engineering Journal, 2020
In this research, analytical and numerical solutions are studied of a two–dimensional discrete electrical lattice, which is mathematically represented by the modified Zakharov–Kuznetsov equation.
Choonkil Park, Mostafa M.A. Khater, Abdel-Haleem Abdel-Aty, Raghda A.M. Attia, Dianchen Lu   +4 more
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Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions

Forum of Mathematics, Sigma
We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity.
Mihaela Ifrim, Annalaura Stingo
doaj   +1 more source

Investigating traveling wave structures in the van der Waals normal form for fluidized granular matter through the modified S-expansion method

Partial Differential Equations in Applied Mathematics
This research discovers traveling wave solutions (TWSs) of the van der Waals normal form for fluidized granular matter using the modified S-expansion (MS-E) method.
Hamida Parvin, Md. Nur Alam, Md. Abdullah Bin Masud, Md. Jakir Hossen   +3 more
doaj   +1 more source

Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience

Partial Differential Equations in Applied Mathematics
Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering ...
Md. Nur Alam, Md. Azizur Rahman
doaj   +1 more source

On well-posedness of energy supercritical NLS on product space Rn×T4−n ${\mathbb{R}}^{n}{\times}{\mathbb{T}}^{4-n}$ (n = 0, 1, 2, 3)

Advances in Nonlinear Analysis
We establish the well-posedness theory for the quintic nonlinear Schrödinger equation (NLS) on four-dimensional tori (i.e., T4 ${\mathbb{T}}^{4}$ ), which is an energy-supercritical model. Compared to the recent breakthrough work (B. Kwak and S.
Wang Han, Li Xing, Lyu Ziyue, Zhao Zehua, Zhou Wenyu   +4 more
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Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense

Partial Differential Equations in Applied Mathematics
This study examines how Stratonovich integrals (SIs) affect the solutions of the Heisenberg ferromagnetic spin chain (HFSC) equation using the modified (G'/G)-expansion (MG'/GE) scheme.
Md. Nur Alam
doaj   +1 more source

WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity [PDF]

, 2007
We consider the semi-classical limit for the Gross-Pitaevskii equation. In order to consider non-trivial boundary conditions at infinity, we work in Zhidkov spaces rather than in Sobolev spaces.
Abdullaev, Alazard, Anton, Bethuel, Brenier, Carles, Carles, Colin, Dalfovo, Gallo, Gammal, Gasser, Grenier, Gérard, Josserand, Lannes, Lin, Majda, Michinel, Métivier, Pitaevskii, Rémi Carles, Sideris, Taylor, Thomann, Thomas Alazard, Zhidkov   +26 more
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On the continuous resonant equation for NLS: II. Statistical study [PDF]

, 2015
We consider the continuous resonant (CR) system of the 2D cubic nonlinear Schr{\"o}dinger (NLS) equation. This system arises in numerous instances as an effective equation for the long-time dynamics of NLS in confined regimes (e.g. on a compact domain or
Germain, Pierre, Hani, Zaher, Thomann, Laurent   +2 more
core   +3 more sources